Solve for $x$ : $ 3|x - 2| - 6 = 4|x - 2| + 5 $
Solution: Subtract $ {3|x - 2|} $ from both sides: $ \begin{eqnarray} 3|x - 2| - 6 &=& 4|x - 2| + 5 \\ \\ {- 3|x - 2|} && {- 3|x - 2|} \\ \\ -6 &=& 1|x - 2| + 5 \end{eqnarray} $ Subtract $5$ from both sides: $ \begin{eqnarray} -6 &=& 1|x - 2| + 5 \\ \\ {- 5} && {- 5} \\ \\ -11 &=& 1|x - 2| \end{eqnarray} $ Simplify: $ -11 = |x - 2| $ The absolute value cannot be negative. Therefore, there is no solution.